Newton Raphson Method Example

Newton Raphson Method Example INTEGRATED AC/DC POWER SYSTEM USING MODIFIED NEWTON-RAPHSON LOAD FLOW ANALYSIS ABSTRACT The Newton-Raphson method or the other name called Newton Method, is a powerful technique for solving equations numerically. Like so much of the differential calculus, it is based on the simple idea of linear approximation. The Newton Method, properly used, usually homes in on a root with devastating efficiency. In this research, the Newton-Raphson method load flow analysis will be modified. It is modified to attain compatibility for the AC/DC systems with unified DC links in the ac network. The modified Jacobian equation includes the DC real and reactive power at the AC/DC buses and their dependency on the AC system variables. The AC/DC test system with a load flow computation in MATLAB will be evaluated by using modified Newton-Raphson method. INTRODUCTION Electric power transmission was primitively developed with direct current. The availability of transformers and the development and of induction motors at the beginning of the 20th Century, led to greater appeal and use of AC transmission. The research and development on multi-electrode grid controlled mercury arc valve for high powers and voltages was carried out in 1929. There use in conversion processes for transmission and frequency changing was carried out in 1930’s. DC transmission now became practical when long distances were to be covered or where cables were required. After the Second World War, the research on HVDC got stimulated, particularly in Sweden and in Russia. In 1950, a 116 km experimental transmission line was commissioned from Moscow to Kasira at 200 kV [1]. HVDC transmission is now an integral part of the delivery of electricity in many countries throughout the world. In view of rapid growth in demand and supply of electricity, electric power system is becoming increasingly large and more complex. Moreover, regular electric supply is the sheer necessity for growing industry and other fields of life. The power industry planners are demanding stronger trend towards supplying electric power of higher quality by improving the system security and its impact on environment in parallel with pursuit of economy. In real life situation, the criterion of perfection is never met, because there are deviations between the model and reality. Load flow and state estimation analysis are important tools for deciding the stable operation and control of power system as well as future planning of power systems [2, 3]. The first commercial HVDC line built in 1954 was a 98 km submarine cable with ground return between the island of Gotland and the Swedish mainland [4]. Thyristors were applied to DC. Transmission in the late 1960’s and solid state valves became a reality. In 1969, a contract for the Eel River DC. Link in Canada was awarded as the first application of sold state valves for HVDC transmission [4]. PROBLEM STATEMENT Why use DC transmission in the transmission system? This question often asked by the people. Some of people are response that the losses will are lower. Unfortunately, the answer given not correct. Therefore, the level of losses is planed into a transmission system and modulate by the selected conductor size. Either as overhead transmission lines or submarine cables can have lower losses but at higher expense since the larger cross-sectional area will generally result in lower losses but cost more for the DC and AC conductors. It is mostly by economic choice, when converters are used for DC transmission in preference to AC transmission driven by one of the following reasons: An overhead DC transmission line with its towers can be designed to be less costly per unit of length than an equivalent AC line designed to transmit the same level of electric power. However it is more costly at each end of the DC converter stations than the terminating stations of an AC line. Therefore, there is a breakeven distance above which the total cost of DC transmission is less than its AC transmission alternative. Lower visual profile can have by the DC transmission line than an equivalent AC line. Indeed, it lead to a lower environmental impact. There are other environmental advantages to a DC transmission line through the electric and magnetic fields being DC instead of ac. The breakeven distance is lesser than overhead transmission, if transmission is by submarine or underground cable. It is not practicable to consider AC cable systems exceeding 50 km but DC cable transmission systems are in service with length which is in hundreds of kilometers and even distances greater than or equal 600 km have been considered executable. Neighboring networks are not synchronized with some AC electric power systems even though their physical distances between them are quite small. This situation occurs in Japan. It is 60 Hz network for half the country and the 50 Hz system for the other side. It is physically impossible to connect the both of them together by direct AC methods in order to exchange electric power between them. Nevertheless, it is likely to transfer the needed power flow even though the AC systems, if a DC converter station is located in each system with an interconnecting DC link between them indeed connected remain asynchronous [1]. OBJECTIVES The main objectives of this research are: To study the Newton-Raphson method for the load flow analysis. To modified the Newton-Raphson method to attain compatibility for AC/DC systems with integrated DC links in the AC network. SIGNIFICANT OF STUDY Load flow study is a crucial tool that involve with the numerical analysis applied to a power system. A power flow study usually uses simplified notation such as a one-line diagram and per-unit system and focuses on various forms of AC power (i.e. voltages, voltage angles, real power and reactive power) [5]. Normal steady-state operation is how the power system is analyze. Exist a few number of software implementations of power flow studies. Load flow analysis is probably the most important of all network calculations since it concerns the network performance in its normal operating conditions. It is performed to enquire the magnitude and phase angle of the voltage at each bus and the real and reactive power flows in the system components. The important of this study is to attain compatibility for AC/DC systems with integrated DC links in the AC network by using the modification of the Newton-Raphson power flow analysis method. SCOPE OF WORK The scope of this research is to analyze IEEE test system with the modified Newton-Raphson algorithm that will be develop and to solve the HVDC link power system load flow. This algorithm will be develop from the Newton-Raphson equation and some other equation from the DC link equations. The Jacobian equation for the AC power flow is altered to attain compatibility for systems with integrated DC link(s) in the AC network. Treated as voltage dependent PQ-buses are the converters. This grant the DC variables to be included in the power flow equations. Both the AC network and the DC link will be comprise by the new residual vector and Jacobian matrix [6]. LITERATURE REVIEW The studies of integrated ac/dc power system, their advantages and analysis of load flow in integrated ac/dc power system and their implementation is much developed here the literature review on these aspects is briefly summarized as: K. Ayan, U. Arifoglu, U. Kilic represent the Load Flow (LF) analysis of pure AC power systems is solved saperately. It is by numerical analysis methods and the heuristic methods. The load flow of integrated ac/dc power systems only has been implementing by numerical methods so far. A lot of methods to implement load flow analysis of integrated ac/dc power systems in literature. Examples of these methods are Newton-Raphson, Fast Decoupled and Broyden. By using Genetic Algorithm the consecutive load flow analysis of AC/DC system is implemented. The suggest method is examine on IEEE 9-bus test system. Heuristic method is apply for load flow analysis of the integrated AC/DC power systems for the first time [7]. Panosyan and Oswald presented the model of a two-terminal HVDC link and its integration into the Newton-Raphson method for the load flow analysis taking into consideration the control strategies of the HVDC converter stations. It is suggested that the simplest way of integrating a dc link into the ac load flow is by representing it by constant active and reactive power injections at the two terminal buses in the ac systems. Thus the two terminal ac/dc buses are delineate as a PQ-bus with a constant voltage independent active and reactive power [8]. Sanghavi and Banerjee suggested a sequential approach for performing the load flow analysis of an integrated ac/dc power system. In this approach a simplified model of the dc link has been developed and the means of integrating the link equation with a standard ac load flow program has been explained. in this model minimum amount of modifications have been made with a standard ac load flow program [3]. Mobarak presented the well-known Newton-Raphson method for the load flow analysis of system consisting of HVDC link. The original NR method is modified to attain compatibility for AC/DC systems with integrated DC links in the AC network. The altered Jacobian equation includes the DC real and reactive power at the AC/DC buses and the dependency on the AC system variables [9]. Marsafawy and Mathur proposed a new method for the load-flow calculations of, integrated AC/DC systems. They proposed use of fast decoupled load flow method, which handles all AC/DC equations simultaneously, and fully exploits the sparsity techniques. They have shown application of the technique on two systems. The systems are one with a point to-point DC transmission and the other with a 3-terminal mesh HVDC sub-system. It was a fast technique for load-flow studies of an integrated AC/DC system [10]. Â   METHODOLOGY Definition of Terms/Concepts MATLAB: MATLABÂ ®is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, data can be analyze, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable us to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages. Newton-Raphson Equation: Power flow equations formulated in polar form. Expressing in polar form; Separating the real and imaginary parts; Expanding equation above in Taylors series The Jacobian matrix; DC Link Equation: Suppose the rectifier maintains constant current (CC), the inverter operates with constant extinction angle (CEA), maintaining adequate commutation margin under normal operation. That is: If we assume the rectifier maintains constant current (CC), the inverter operates with constant voltage (CV), maintaining adequate commutation margin under normal operation. That is: CONCLUSION In a nutshell, the objective of this study will be achieved after all the research have been done. The Newton-Raphson method will be study and will be applied in the load flow analysis. Then, the Newton-Raphson method will be modified and applied in the AC/DC systems with the integrated DC links in the AC network to achieve it compatibility. The research will able to make the calculation for the AC/DC systems with integrated DC links in the AC network become easy. A new method to include dc systems in power flow calculations will be proposed. The method is more efficient than previous methods and more importantly, the method is easy to implement and developments of ac power flow solution techniques can be combined with the other method. REFERENCES [1]D. A. Woodford, HVDC transmission, Manitoba HVDC Research Centre, pp. 400-1619, 1998. [2]J. Arrillaga and P. Bodger, Integration of h.v.d.c. links with fast-decoupled load-flow solutions, Electrical Engineers, Proceedings of the Institution of, vol. 124, pp. 463-468, 1977. [3]H. A. Sanghavi and S. K. Banerjee, Load flow analysis of integrated AC-DC power systems, in TENCON 89. Fourth IEEE Region 10 International Conference, 1989, pp. 746-751. [4]H. Sato and J. Arrillaga, Improved load-flow techniques for integrated a.c.-d.c. systems, Electrical Engineers, Proceedings of the Institution of, vol. 116, pp. 525-532, 1969. [5]S. Gupta and S. K. Jain, Power flow analysis of system with HVDC link, 2012. [6]O. Osaloni and G. Radman, Integrated AC/DC systems power flow solution using Newton-Raphson and Broyden approaches, in System Theory, 2005. SSST05. Proceedings of the Thirty-Seventh Southeastern Symposium on, 2005, pp. 225-229. [7]K. Ayan, U. Arifoglu, and U. Kilic, Integrated AC/DC systems Load Flow using Genetic Algorithm, in Power Engineering and Optimization Conference (PEOCO), 2011 5th International, 2011, pp. 404-409. [8]A. Panosyan and B. Oswald, Modified Newton-Raphson load flow analysis for integrated AC/DC power systems, in Universities Power Engineering Conference, 2004. UPEC 2004. 39th International, 2004, pp. 1223-1227. [9]Y. A. Mobarak, Notice of Violation of IEEE Publication PrinciplesModified load flow analysis for integrated AC/DC power systems, in Power System Conference, 2008. MEPCON 2008. 12th International Middle-East, 2008, pp. 402-405. [10]M. M. El-Marsafawy and R. M. Mathur, A New, Fast Technique for Load-Flow Solution of Integrated Multi-Terminal DC/AC Systems, Power Apparatus and Systems, IEEE Transactions on, vol. PAS-99, pp. 246-255, 1980.

Year Round Education Program

Imagine a child, on a hot summer day†¦ no baseball, no swimming, no picnics or amusement park rides. Instead of spending time doing all of the things kids like to during summer vacations, this child, is attending school. Year round education (YRE) has been around since 1904, with 3,000 schools and 2 million students currently using the program (National Association). Students in year round schools go to school the same 180 days that traditional schools attend. In YRE, the summer vacation is eliminated, replacing it with shorter, more frequent breaks. There is a number of ways the year round school can operate, including: 90/30, 45/15, and 60/20. The most popular of these calendars is the 45/15, where the year is divided into 4 nine week terms, separated by 4 three week vacations (National Association). YRE has been a debated issue in education almost since it began. Supporters of YRE say this schedule improves the learning process. The biggest debate, however, comes from the parents and teachers who believe there are no proven studies that YRE helps the learning process at all. So, is year round schooling a good choice for the education of your children? YRE will not only hurt the education system, but it will create chaos for the lives of the students attending and their families. Supporters of YRE believe year round schools are more cost effective than traditional schools. With population in some districts rising rapidly, YRE is said to reduce overcrowding of schools and classrooms. In many cases, school calendars are changed in response to population growth. By running schools all year, districts can pack in more students and postpone building new schools (Endless Summer). Supporters of YRE say that by staggering vacations and schedules, schools can increase capacity by 25-50 percent (Should Kids go). Supporters argue that the costs for the transition form a traditional calendar to year round schools are modest compared to the construction costs of new schools (Inger, Morton). However, those against YRE feel that expenses will only be reduced temporarily. According to a â€Å"Year Round Education Study† conducted by the Lewisville, Texas Independent School District, â€Å"Findings of a year-long study concluded that there is no financial benefit to operating a Single Track System. The system would cause a modest increase in operational expenses without providing any instructional benefits† (Time to Learn). In Iowa, the Carroll School Board found that the costs of the district moving to a year round education system could range from $16,786 to $32,412. Taylor Elementary School, in Cedar Rapids, spends more money according to the classroom teachers that any other elementary school. Schools in Davenport reported that the switch to YRE will cost an additional $36,000 in salaries, $3000 per year for equipment, and supplies, and $22,300 as a one time expense for teacher training. Plus, the move to YRE would also cost the district an extra $92,626 to fully air condition the school building. In Des Moines, Moulten schools spend about $80,000 annually for year round schooling. If YRE were implemented, Indianola school districts would spend an additional $3,655 for middle school and $5,000 for elementary school to pay for the additional secretarial, administrative, and custodial time during the summer (Time to Learn). Costs will not only be incurred with the schools, but also with the state and with taxpayers. Cost savings for one of these groups may create cost increases for the other (Naylor, Charlie). Contrary to what supporters of YRE claim, there are definitely extra costs to implementing and maintaining a year round education system. Supporters of YRE say that year round schools would promote continuous learning. The belief is that students forget a lot of what they learn while on long summer vacations. This is seen more in slower learning students and for those who know English as their second language. It is also thought that because students retain more when the learning process is interrupted for only short periods of time, teachers in year round schools need to spend less time reviewing pre-vacation material (Inger, Morton). Although this seems true, opponents believe that there is research that needs to be addressed. Mary Lee Smith and Gene V. Glass have done extensive research in year round schools since 1974. In a study conducted by Smith and Glass, in a school district in Colorado, the learning loss in the students was evaluated. They found that although teachers in year round schools spent less time reviewing pre-vacation material than teachers in traditional schools did, the actual achievement differences were insignificant on tests designed specifically to measure district objectives (Glass, Gene V). According to Don Patterson, a member of the Albuquerque, New Mexico School Board that tried and rejected year round schooling, â€Å"Short term memory loss is very acute. Studies show that the only discernible summer loss occurs in the first two to three weeks. So, by introducing all these multiple breaks, all you†re doing is maximizing forgetting. † It has also been proven that forgetting and relearning are part of the learning process. Gaps in student†s learning begin with loss of context retention in the subject area, which begins within 24-48 hours, unless the new information is reinforced or applied immediately. After a month without reinforcement, about 80% of what a student has learned is recently lost. Research indicates what we retain depends on student motivation and teacher-effectiveness and isn†t limited to a time factor (Time to Learn). It is quite obvious that YRE does not improve the learning process, as those who support YRE claim. Supporters of the year round school system believe there are many benefits in the program for students and teachers. Advocates of YRE say families have greater flexibility in planning vacations that often cost less. Parents that support YRE feel that the shorter, more frequent vacations allowed students to remain focused and enthusiastic (Prisoners of Time). Angie Maniscalco, a 5th grade student at Fairmount Elementary in St. Louis, says, â€Å"Kids should go to school nine weeks and be off three because, kids get bored in the summer. They get sick of swimming every single day going skating or basically doing anything. I go to school for nine weeks, then get off three† (Should Schools). Supporters also believe parents who are working outside the home can take advantage of year-round care for their children. Teachers that support the idea of YRE feel that the more frequent breaks reduce burnout, and that the frequent breaks during the school year enable teachers to visit and learn from other programs and other teachers (Prisoners of Time). Those against YRE have different views about what year-round schooling will do for the students and the teachers. In year round schools, middle, elementary and high school students often have different schedules. While vacationing in the off-season may work well, when children are on different schedules, vacations can be more of a problem. YRE can certainly disrupt family life. With different ages of students, vacations are difficult to schedule. For example, children on non-traditional schedules may miss out on Boy Scout Camp, because their summer vacation falls in the month of August and the activity is programmed for July. School activities can suffer as well. One study found that band, chorus, drama, and student government were particularly hit hard (Never Ending School). While there may be some benefits to YRE, it is obvious that there are many situations where the year round calendar will cause confusion in the lives of those involved. Perhaps the most debated issue in YRE is that of the achievement scores. Supporters of YRE claim that student performance in year round schools is much greater. They believe that year round schools will yield higher achievement scores that traditional schools. Many advocates for YRE claim there are studies by the National Association for Year Round Education that report that year round schools have a very positive impact on student grades. Although supporters boast high achievement scores on tests, and higher student grades, those against YRE disagree (Year Round Education: Is). Critics of YRE say there is no evidence for higher academic gains under YRE as compared to traditional schools. Studies and test scores repeatedly show little improvement by students in year round schools. When test scores do increase, many educators hesitate to attribute increases to the new calendar (Time to Learn). Many of these studies, have been conducted by the National Association for Year Round Education (NAYRE), a highly biased organization, whose consultants earn significant amounts of income by promotion YRE. Robert Rosenfield, a systems analyst from Potomac, Maryland, was so concerned at what he considered to be misrepresented data by the NAYRE that he analyzed a substantial number of YRE evaluations in a 1994 paper. He concluded, â€Å"Each study presented in the NAYRE review has either been incompletely characterized, or otherwise contradicted by other studies within the same state or district. Nothing in the NAYRE review demonstrates any academic achievement gain by changing to a year-round calendar. In a 1993 Resnik study of Oakland Unified School District, California, concluded, â€Å"Students at year-round schools show on average a lower academic achievement level than those at other schools, and their achievement has decreased for the period, while it increased for schools in the regular calendar. † Overall, as you can see, there is little difference in student achievement between year-round and traditional calendars (Year Round Education: Is). As evidence has shown, year round education will not improve the education of our children. YRE will cost more money for schools. YRE will not promote continuous learning. YRE won†t create benefits for students and teachers, but will create chaos in the lives of the people around them. Achievement scores in schools with YRE will not increase, but in fact, in some cases, get worse. A few spoken views on YRE say it best. Sheila Duty Gibson says, â€Å"Many students show that year-round schools do not improve education. Changing the days students attend school does not address what many believe are the real problems in education such as a lack of parental involvement, teacher development, effective teaching methods and curriculum. An anonymous editorial in a North Carolina newspaper says, â€Å"It†s time to face the truth. The year-round schedule is a personal preference, not the answer to our educational problems. Year-round school doesn†t work for everyone. † Executive Editor of Elizabethton Star in Tennessee, said it well when he said, â€Å"Summertime offers our youngsters an extended time to experience life in such a way that will never again be afforded. If we are going to do anything with respect to school scheduling, we should extend the summer vacation to Labor Day† (Time to Learn).

A Darwinian Reading of Great Expectations - 700 Words

A Darwinian Reading of Great Expectations Goldie Morgentaler, assistant professor of English at the University of Lethbridge, compares Charles Dickens’s Great Expectations with Charles Darwin’s The Origin of Species, suggesting that a Darwinian influence can be found within its text. Morgentaler argues her point using the time the two books were written and the sudden disregard of heredity as a formative influence of human identity in Dickens’s writing. Morgentaler’s arguments are somewhat weak in evidence but I agree that it probably isn’t a coincidence that Dickens’s writing on this subject matter changed around the same time as Darwin’s book was published. I will engage some of the points that I thought were strongest in favor†¦show more content†¦With it being â€Å"in everybody’s hands† there is little doubt that Dickens had not heard about or even talked with others about this very controversial topic an d book. Another piece of strong evidence was in Dickens’s journal, All the Year Round, where there were anonymous pieces published with Darwinian themes. Another strong piece of evidence was that a copy of Darwin’s book was found in Dickens’s library after his death (709). While all of this may be coincidence and circumstantial, Morgentaler did give stronger textual evidence for her argument. There are concepts that have broad evolutionary implications that Morgentaler says gives Great Expectations reasons for having a Darwinian reading. Morgentaler says, â€Å"†¦The idea of the primitive or low and its relationship to ‘civilized’ society; the idea of adaptation, of what is fit and not fit; and, finally, the conception of time as moving in one direction only—into the future—rather than being a reanimation of the past† (712). In the case of Pip and Magwitch money has replaced hereditary DNA. According to Morgentaler, à ¢â‚¬Å"In this father-son relationship, money substitutes for semen as the stuff out of which life is created† (712). It was not hereditary that made Pip a gentleman, but a convict with money. The same can be said of Estella and Miss Havisham—Estella became what her adopted mother trained her to be. It has turnedShow MoreRelated Darwinism in Great Expectations by Charles Dickens Essay examples1550 Words   |  7 Pages Few people argue that Great Expectations, one of Dickens’s later novels, is a Darwinian work. Goldie Morgentaler, in her essay â€Å"Meditating on the Low: A Darwinian Reading of Great Expectations,† is one of those few. 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Quantifier - Definition and Examples

In grammar, a quantifier is a type of determiner (such as all, some, or much) that expresses a relative or indefinite indication of quantity. Quantifiers usually appear in front of nouns (as in all children), but they may also function as pronouns (as in All have returned). A complex quantifier is a phrase (such as a lot of) that functions as a quantifier. Examples and Observations I believe that every person is born with talent.  (Maya Angelou)Most of the people who will walk after me will be children, so make the beat keep time with short steps. (Hans Christian Andersen, in the instructions for the music for his funeral)Many books require no thought from those who read them, and for a very simple reason: they made no such demand upon those who wrote them. (Charles Caleb Colton, Lacon, or Many things in Few Words, 1820)All politicians should have three hats: one to throw into the ring, one to talk through, and one to pull rabbits out of if elected. (Carl Sandburg)Ive had a lot of worries in my life, most of which never happened. (attributed to Mark Twain, among others) Meanings of Quantifiers Quantifiers can be classified in terms of their meaning. Some quantifiers have a meaning of inclusiveness. That is, they refer to an entire group. Both refers to two members of a group of two, few to a subgroup of the entire group, and all to the totality of members of a group of unspecified size. Every and each refer to single members of a group. The difference between all, a few, and both on the one hand and each and every, is reflected in subject-verb agreement​Other quantifiers are noninclusive and have a meaning related to size or quantity. These quantifiers can be classified by the relative size they indicate. For example, many and much refer to large quantities, some to a moderate quantity, and little and few to small quantities . . .. (Ron Cowan, The Teachers Grammar of English: A Course Book and Reference Guide. Cambridge University Press, 2008) Partitives and Quantifiers: Agreement There is, in fact, a somewhat fuzzy distinction between partitive structures and inclusives and Quantifiers formed with of. In a clause such as a lot of students have arrived it is the noun students which determines number agreement on the Finite (have - plural). It is not normally possible to say *a lot of students has arrived. Therefore students is the head of the noun group and a lot of is a complex Quantifier. Similarly, it is also normal to say a number of students have arrived not a number of students has arrived, that is, to treat a number of as a complex Quantifier. . . .For beginning learners, it may be best to introduce expressions such as a lot of and a number of as complex Quantifiers but in other cases to err on the prescriptive side and encourage agreement with the noun preceding of. (Graham Lock, Functional English Grammar. Cambridge University Press, 1996) Count Nouns, Mass Nouns, and Quantifiers Count nouns (e.g. diamond, bottle, book, board, waiter, table, cat, bush, truck, house) and mass nouns (e.g. gold, coffee, paper, wood, meat, air, water, coal, smoke, blood, wine) differ grammatically in the range of articles and quantifiers they occur with. For instance, count nouns occur with the indefinite article a but not with the complex quantifier a lot of: a diamond, *a lot of diamond. Mass nouns do the opposite: a lot of gold, *a gold. (Ronald W. Langacker, Linguistic Manifestations of the Space-Time (Dis)Analogy. Space and Time in Languages and Cultures: Language, Culture, and Cognition, ed. by Luna Filipović and Katarzyna M. Jaszczolt. John Benjamins, 2012) Zero Plurals After numerals or quantifiers, count nouns may have a zero plural (the same form as in the singular): thirty year, many mile.​  (Sidney Greenbaum, Oxford English Grammar. Oxford University Press, 1996) Also Known As: quantifying determiner